Officers investigating criminal activity (for these purposes, I include traffic infractions) can turn around to stop an alleged offender, yes. In order to stop someone, they need a legal basis to do so. A broken tail light, as petty as that sounds, is a traffic infraction and thus a legal basis to stop someone. In some states, the issue might be thornier if the stop was a pretext; but that doesn't sound like the issue here (you have only cited the broken light). If there is more to the story, then you should contact a Wyoming attorney who can discuss the Wyoming legal issues in detail.
I assume you suspect he pulled you over because you are from Colorado, and may have been in possession of marijuana. Many states are having problems with Colorado drivers. But the cop will undoubtedly say he pulled you over because of your tail light, which is entirely permissible.
Yes. Your tail light was out, and as such is a violation of the traffic code. An officer can stop a motor vehicle for any infraction of the law, no matter how minor (cracked windshields are a favorite). There is no such animal as a pretext stop in Wyoming so long as there is an infraction of the law. I would imagine he was hoping to find that you had Marijuana in your car as you are from the great and marijuana legal state of Colorado.